Properties

Label 69.6.c.b.68.5
Level $69$
Weight $6$
Character 69.68
Analytic conductor $11.066$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 69.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0664835671\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 68.5
Character \(\chi\) \(=\) 69.68
Dual form 69.6.c.b.68.27

$q$-expansion

\(f(q)\) \(=\) \(q-8.75944i q^{2} +(10.6432 + 11.3896i) q^{3} -44.7279 q^{4} -43.1688 q^{5} +(99.7663 - 93.2285i) q^{6} -151.444i q^{7} +111.489i q^{8} +(-16.4449 + 242.443i) q^{9} +O(q^{10})\) \(q-8.75944i q^{2} +(10.6432 + 11.3896i) q^{3} -44.7279 q^{4} -43.1688 q^{5} +(99.7663 - 93.2285i) q^{6} -151.444i q^{7} +111.489i q^{8} +(-16.4449 + 242.443i) q^{9} +378.135i q^{10} -610.914 q^{11} +(-476.047 - 509.431i) q^{12} +132.232 q^{13} -1326.57 q^{14} +(-459.454 - 491.674i) q^{15} -454.710 q^{16} -1720.33 q^{17} +(2123.67 + 144.048i) q^{18} +554.256i q^{19} +1930.85 q^{20} +(1724.89 - 1611.85i) q^{21} +5351.26i q^{22} +(2536.22 - 62.8693i) q^{23} +(-1269.81 + 1186.60i) q^{24} -1261.46 q^{25} -1158.28i q^{26} +(-2936.35 + 2393.07i) q^{27} +6773.79i q^{28} -7005.84i q^{29} +(-4306.79 + 4024.56i) q^{30} +4819.56 q^{31} +7550.66i q^{32} +(-6502.07 - 6958.05i) q^{33} +15069.2i q^{34} +6537.67i q^{35} +(735.543 - 10844.0i) q^{36} -1324.61i q^{37} +4854.97 q^{38} +(1407.37 + 1506.07i) q^{39} -4812.84i q^{40} +231.107i q^{41} +(-14118.9 - 15109.1i) q^{42} -18413.9i q^{43} +27324.9 q^{44} +(709.905 - 10466.0i) q^{45} +(-550.700 - 22215.8i) q^{46} -11782.0i q^{47} +(-4839.57 - 5178.96i) q^{48} -6128.42 q^{49} +11049.7i q^{50} +(-18309.8 - 19593.9i) q^{51} -5914.46 q^{52} +1891.55 q^{53} +(20961.9 + 25720.8i) q^{54} +26372.4 q^{55} +16884.4 q^{56} +(-6312.74 + 5899.05i) q^{57} -61367.2 q^{58} +7712.06i q^{59} +(20550.4 + 21991.5i) q^{60} -1208.84i q^{61} -42216.7i q^{62} +(36716.6 + 2490.48i) q^{63} +51588.8 q^{64} -5708.30 q^{65} +(-60948.6 + 56954.5i) q^{66} +41089.5i q^{67} +76946.8 q^{68} +(27709.5 + 28217.3i) q^{69} +57266.4 q^{70} -8193.96i q^{71} +(-27029.7 - 1833.42i) q^{72} -78243.7 q^{73} -11602.9 q^{74} +(-13425.9 - 14367.5i) q^{75} -24790.7i q^{76} +92519.5i q^{77} +(13192.3 - 12327.8i) q^{78} -77477.3i q^{79} +19629.3 q^{80} +(-58508.1 - 7973.88i) q^{81} +2024.37 q^{82} +17093.4 q^{83} +(-77150.5 + 72094.7i) q^{84} +74264.7 q^{85} -161296. q^{86} +(79793.5 - 74564.5i) q^{87} -68110.1i q^{88} +135956. q^{89} +(-91676.0 - 6218.37i) q^{90} -20025.8i q^{91} +(-113439. + 2812.01i) q^{92} +(51295.5 + 54892.7i) q^{93} -103204. q^{94} -23926.5i q^{95} +(-85998.8 + 80363.1i) q^{96} +75181.6i q^{97} +53681.6i q^{98} +(10046.4 - 148112. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 408 q^{4} - 528 q^{6} - 444 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 408 q^{4} - 528 q^{6} - 444 q^{9} - 2484 q^{12} + 520 q^{13} + 4936 q^{16} + 7188 q^{18} + 18660 q^{24} + 36032 q^{25} - 22032 q^{27} + 6544 q^{31} - 33912 q^{36} - 63912 q^{39} + 54328 q^{46} + 88284 q^{48} - 207664 q^{49} + 46296 q^{52} - 38628 q^{54} - 139296 q^{55} - 184144 q^{58} + 486584 q^{64} - 113580 q^{69} + 37176 q^{70} - 15504 q^{72} - 93896 q^{73} + 249840 q^{75} + 368028 q^{78} - 339372 q^{81} - 23512 q^{82} + 259584 q^{85} + 509928 q^{87} + 82740 q^{93} - 562000 q^{94} + 1404 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 8.75944i 1.54847i −0.632901 0.774233i \(-0.718136\pi\)
0.632901 0.774233i \(-0.281864\pi\)
\(3\) 10.6432 + 11.3896i 0.682761 + 0.730642i
\(4\) −44.7279 −1.39775
\(5\) −43.1688 −0.772227 −0.386113 0.922451i \(-0.626183\pi\)
−0.386113 + 0.922451i \(0.626183\pi\)
\(6\) 99.7663 93.2285i 1.13137 1.05723i
\(7\) 151.444i 1.16818i −0.811690 0.584088i \(-0.801452\pi\)
0.811690 0.584088i \(-0.198548\pi\)
\(8\) 111.489i 0.615895i
\(9\) −16.4449 + 242.443i −0.0676743 + 0.997707i
\(10\) 378.135i 1.19577i
\(11\) −610.914 −1.52229 −0.761146 0.648580i \(-0.775363\pi\)
−0.761146 + 0.648580i \(0.775363\pi\)
\(12\) −476.047 509.431i −0.954326 1.02125i
\(13\) 132.232 0.217009 0.108505 0.994096i \(-0.465394\pi\)
0.108505 + 0.994096i \(0.465394\pi\)
\(14\) −1326.57 −1.80888
\(15\) −459.454 491.674i −0.527246 0.564221i
\(16\) −454.710 −0.444053
\(17\) −1720.33 −1.44374 −0.721872 0.692026i \(-0.756718\pi\)
−0.721872 + 0.692026i \(0.756718\pi\)
\(18\) 2123.67 + 144.048i 1.54492 + 0.104791i
\(19\) 554.256i 0.352230i 0.984370 + 0.176115i \(0.0563530\pi\)
−0.984370 + 0.176115i \(0.943647\pi\)
\(20\) 1930.85 1.07938
\(21\) 1724.89 1611.85i 0.853518 0.797585i
\(22\) 5351.26i 2.35722i
\(23\) 2536.22 62.8693i 0.999693 0.0247810i
\(24\) −1269.81 + 1186.60i −0.449999 + 0.420509i
\(25\) −1261.46 −0.403666
\(26\) 1158.28i 0.336031i
\(27\) −2936.35 + 2393.07i −0.775172 + 0.631750i
\(28\) 6773.79i 1.63281i
\(29\) 7005.84i 1.54691i −0.633851 0.773455i \(-0.718527\pi\)
0.633851 0.773455i \(-0.281473\pi\)
\(30\) −4306.79 + 4024.56i −0.873677 + 0.816423i
\(31\) 4819.56 0.900748 0.450374 0.892840i \(-0.351291\pi\)
0.450374 + 0.892840i \(0.351291\pi\)
\(32\) 7550.66i 1.30350i
\(33\) −6502.07 6958.05i −1.03936 1.11225i
\(34\) 15069.2i 2.23559i
\(35\) 6537.67i 0.902097i
\(36\) 735.543 10844.0i 0.0945915 1.39454i
\(37\) 1324.61i 0.159069i −0.996832 0.0795343i \(-0.974657\pi\)
0.996832 0.0795343i \(-0.0253433\pi\)
\(38\) 4854.97 0.545416
\(39\) 1407.37 + 1506.07i 0.148166 + 0.158556i
\(40\) 4812.84i 0.475611i
\(41\) 231.107i 0.0214710i 0.999942 + 0.0107355i \(0.00341729\pi\)
−0.999942 + 0.0107355i \(0.996583\pi\)
\(42\) −14118.9 15109.1i −1.23503 1.32164i
\(43\) 18413.9i 1.51871i −0.650675 0.759357i \(-0.725514\pi\)
0.650675 0.759357i \(-0.274486\pi\)
\(44\) 27324.9 2.12778
\(45\) 709.905 10466.0i 0.0522599 0.770456i
\(46\) −550.700 22215.8i −0.0383726 1.54799i
\(47\) 11782.0i 0.777990i −0.921240 0.388995i \(-0.872822\pi\)
0.921240 0.388995i \(-0.127178\pi\)
\(48\) −4839.57 5178.96i −0.303182 0.324444i
\(49\) −6128.42 −0.364635
\(50\) 11049.7i 0.625063i
\(51\) −18309.8 19593.9i −0.985733 1.05486i
\(52\) −5914.46 −0.303324
\(53\) 1891.55 0.0924973 0.0462487 0.998930i \(-0.485273\pi\)
0.0462487 + 0.998930i \(0.485273\pi\)
\(54\) 20961.9 + 25720.8i 0.978244 + 1.20033i
\(55\) 26372.4 1.17556
\(56\) 16884.4 0.719474
\(57\) −6312.74 + 5899.05i −0.257354 + 0.240489i
\(58\) −61367.2 −2.39534
\(59\) 7712.06i 0.288430i 0.989546 + 0.144215i \(0.0460657\pi\)
−0.989546 + 0.144215i \(0.953934\pi\)
\(60\) 20550.4 + 21991.5i 0.736956 + 0.788637i
\(61\) 1208.84i 0.0415953i −0.999784 0.0207977i \(-0.993379\pi\)
0.999784 0.0207977i \(-0.00662058\pi\)
\(62\) 42216.7i 1.39478i
\(63\) 36716.6 + 2490.48i 1.16550 + 0.0790555i
\(64\) 51588.8 1.57437
\(65\) −5708.30 −0.167580
\(66\) −60948.6 + 56954.5i −1.72228 + 1.60942i
\(67\) 41089.5i 1.11826i 0.829080 + 0.559131i \(0.188865\pi\)
−0.829080 + 0.559131i \(0.811135\pi\)
\(68\) 76946.8 2.01799
\(69\) 27709.5 + 28217.3i 0.700658 + 0.713498i
\(70\) 57266.4 1.39687
\(71\) 8193.96i 0.192907i −0.995337 0.0964535i \(-0.969250\pi\)
0.995337 0.0964535i \(-0.0307499\pi\)
\(72\) −27029.7 1833.42i −0.614483 0.0416803i
\(73\) −78243.7 −1.71847 −0.859235 0.511581i \(-0.829060\pi\)
−0.859235 + 0.511581i \(0.829060\pi\)
\(74\) −11602.9 −0.246312
\(75\) −13425.9 14367.5i −0.275607 0.294935i
\(76\) 24790.7i 0.492328i
\(77\) 92519.5i 1.77831i
\(78\) 13192.3 12327.8i 0.245519 0.229429i
\(79\) 77477.3i 1.39671i −0.715751 0.698356i \(-0.753915\pi\)
0.715751 0.698356i \(-0.246085\pi\)
\(80\) 19629.3 0.342910
\(81\) −58508.1 7973.88i −0.990840 0.135038i
\(82\) 2024.37 0.0332472
\(83\) 17093.4 0.272354 0.136177 0.990685i \(-0.456518\pi\)
0.136177 + 0.990685i \(0.456518\pi\)
\(84\) −77150.5 + 72094.7i −1.19300 + 1.11482i
\(85\) 74264.7 1.11490
\(86\) −161296. −2.35168
\(87\) 79793.5 74564.5i 1.13024 1.05617i
\(88\) 68110.1i 0.937573i
\(89\) 135956. 1.81938 0.909691 0.415286i \(-0.136319\pi\)
0.909691 + 0.415286i \(0.136319\pi\)
\(90\) −91676.0 6218.37i −1.19303 0.0809227i
\(91\) 20025.8i 0.253505i
\(92\) −113439. + 2812.01i −1.39732 + 0.0346376i
\(93\) 51295.5 + 54892.7i 0.614996 + 0.658124i
\(94\) −103204. −1.20469
\(95\) 23926.5i 0.272001i
\(96\) −85998.8 + 80363.1i −0.952388 + 0.889976i
\(97\) 75181.6i 0.811302i 0.914028 + 0.405651i \(0.132955\pi\)
−0.914028 + 0.405651i \(0.867045\pi\)
\(98\) 53681.6i 0.564625i
\(99\) 10046.4 148112.i 0.103020 1.51880i
\(100\) 56422.2 0.564222
\(101\) 182646.i 1.78159i −0.454410 0.890793i \(-0.650150\pi\)
0.454410 0.890793i \(-0.349850\pi\)
\(102\) −171631. + 160384.i −1.63341 + 1.52637i
\(103\) 60433.1i 0.561283i 0.959813 + 0.280642i \(0.0905472\pi\)
−0.959813 + 0.280642i \(0.909453\pi\)
\(104\) 14742.4i 0.133655i
\(105\) −74461.3 + 69581.7i −0.659109 + 0.615917i
\(106\) 16569.0i 0.143229i
\(107\) −19007.4 −0.160495 −0.0802477 0.996775i \(-0.525571\pi\)
−0.0802477 + 0.996775i \(0.525571\pi\)
\(108\) 131337. 107037.i 1.08349 0.883026i
\(109\) 95078.3i 0.766505i 0.923644 + 0.383253i \(0.125196\pi\)
−0.923644 + 0.383253i \(0.874804\pi\)
\(110\) 231008.i 1.82031i
\(111\) 15086.8 14098.1i 0.116222 0.108606i
\(112\) 68863.3i 0.518732i
\(113\) 68259.2 0.502881 0.251440 0.967873i \(-0.419096\pi\)
0.251440 + 0.967873i \(0.419096\pi\)
\(114\) 51672.4 + 55296.1i 0.372389 + 0.398503i
\(115\) −109485. + 2713.99i −0.771989 + 0.0191366i
\(116\) 313356.i 2.16219i
\(117\) −2174.54 + 32058.7i −0.0146860 + 0.216512i
\(118\) 67553.3 0.446624
\(119\) 260535.i 1.68655i
\(120\) 54816.2 51224.0i 0.347501 0.324729i
\(121\) 212165. 1.31738
\(122\) −10588.8 −0.0644089
\(123\) −2632.21 + 2459.71i −0.0156876 + 0.0146596i
\(124\) −215569. −1.25902
\(125\) 189358. 1.08395
\(126\) 21815.2 321617.i 0.122415 1.80473i
\(127\) −162337. −0.893116 −0.446558 0.894755i \(-0.647350\pi\)
−0.446558 + 0.894755i \(0.647350\pi\)
\(128\) 210268.i 1.13435i
\(129\) 209727. 195983.i 1.10964 1.03692i
\(130\) 50001.5i 0.259492i
\(131\) 120535.i 0.613669i −0.951763 0.306835i \(-0.900730\pi\)
0.951763 0.306835i \(-0.0992699\pi\)
\(132\) 290824. + 311219.i 1.45276 + 1.55464i
\(133\) 83939.0 0.411466
\(134\) 359921. 1.73159
\(135\) 126759. 103306.i 0.598608 0.487854i
\(136\) 191798.i 0.889195i
\(137\) −324305. −1.47623 −0.738113 0.674677i \(-0.764283\pi\)
−0.738113 + 0.674677i \(0.764283\pi\)
\(138\) 247168. 242720.i 1.10483 1.08494i
\(139\) 168785. 0.740964 0.370482 0.928840i \(-0.379193\pi\)
0.370482 + 0.928840i \(0.379193\pi\)
\(140\) 292416.i 1.26090i
\(141\) 134192. 125398.i 0.568432 0.531182i
\(142\) −71774.5 −0.298710
\(143\) −80782.4 −0.330352
\(144\) 7477.65 110241.i 0.0300510 0.443035i
\(145\) 302433.i 1.19456i
\(146\) 685371.i 2.66099i
\(147\) −65226.0 69800.1i −0.248959 0.266417i
\(148\) 59247.1i 0.222338i
\(149\) −346489. −1.27857 −0.639283 0.768971i \(-0.720769\pi\)
−0.639283 + 0.768971i \(0.720769\pi\)
\(150\) −125851. + 117604.i −0.456697 + 0.426769i
\(151\) −484291. −1.72848 −0.864239 0.503082i \(-0.832199\pi\)
−0.864239 + 0.503082i \(0.832199\pi\)
\(152\) −61793.4 −0.216937
\(153\) 28290.6 417083.i 0.0977044 1.44043i
\(154\) 810419. 2.75365
\(155\) −208055. −0.695581
\(156\) −62948.7 67363.1i −0.207098 0.221621i
\(157\) 129167.i 0.418218i 0.977892 + 0.209109i \(0.0670564\pi\)
−0.977892 + 0.209109i \(0.932944\pi\)
\(158\) −678658. −2.16276
\(159\) 20132.2 + 21544.0i 0.0631536 + 0.0675824i
\(160\) 325953.i 1.00659i
\(161\) −9521.21 384096.i −0.0289486 1.16782i
\(162\) −69846.7 + 512499.i −0.209102 + 1.53428i
\(163\) −54105.7 −0.159505 −0.0797525 0.996815i \(-0.525413\pi\)
−0.0797525 + 0.996815i \(0.525413\pi\)
\(164\) 10336.9i 0.0300110i
\(165\) 280687. + 300370.i 0.802623 + 0.858909i
\(166\) 149729.i 0.421730i
\(167\) 46358.5i 0.128629i −0.997930 0.0643144i \(-0.979514\pi\)
0.997930 0.0643144i \(-0.0204861\pi\)
\(168\) 179704. + 192306.i 0.491229 + 0.525678i
\(169\) −353808. −0.952907
\(170\) 650517.i 1.72638i
\(171\) −134375. 9114.66i −0.351422 0.0238369i
\(172\) 823617.i 2.12277i
\(173\) 371854.i 0.944620i 0.881433 + 0.472310i \(0.156580\pi\)
−0.881433 + 0.472310i \(0.843420\pi\)
\(174\) −653143. 698947.i −1.63544 1.75013i
\(175\) 191041.i 0.471553i
\(176\) 277789. 0.675979
\(177\) −87837.0 + 82080.9i −0.210739 + 0.196929i
\(178\) 1.19090e6i 2.81725i
\(179\) 320039.i 0.746570i 0.927717 + 0.373285i \(0.121769\pi\)
−0.927717 + 0.373285i \(0.878231\pi\)
\(180\) −31752.5 + 468120.i −0.0730461 + 1.07690i
\(181\) 512556.i 1.16291i −0.813580 0.581453i \(-0.802484\pi\)
0.813580 0.581453i \(-0.197516\pi\)
\(182\) −175415. −0.392544
\(183\) 13768.2 12865.9i 0.0303913 0.0283997i
\(184\) 7009.23 + 282760.i 0.0152625 + 0.615706i
\(185\) 57181.9i 0.122837i
\(186\) 480830. 449320.i 1.01908 0.952299i
\(187\) 1.05098e6 2.19780
\(188\) 526983.i 1.08743i
\(189\) 362417. + 444694.i 0.737995 + 0.905537i
\(190\) −209583. −0.421185
\(191\) −269982. −0.535489 −0.267745 0.963490i \(-0.586278\pi\)
−0.267745 + 0.963490i \(0.586278\pi\)
\(192\) 549070. + 587575.i 1.07492 + 1.15030i
\(193\) −624538. −1.20688 −0.603442 0.797407i \(-0.706205\pi\)
−0.603442 + 0.797407i \(0.706205\pi\)
\(194\) 658549. 1.25627
\(195\) −60754.5 65015.1i −0.114417 0.122441i
\(196\) 274111. 0.509667
\(197\) 733978.i 1.34747i −0.738975 0.673733i \(-0.764690\pi\)
0.738975 0.673733i \(-0.235310\pi\)
\(198\) −1.29738e6 88000.8i −2.35181 0.159523i
\(199\) 896250.i 1.60434i 0.597095 + 0.802170i \(0.296321\pi\)
−0.597095 + 0.802170i \(0.703679\pi\)
\(200\) 140638.i 0.248616i
\(201\) −467991. + 437323.i −0.817048 + 0.763505i
\(202\) −1.59988e6 −2.75872
\(203\) −1.06099e6 −1.80706
\(204\) 818960. + 876392.i 1.37780 + 1.47443i
\(205\) 9976.60i 0.0165805i
\(206\) 529360. 0.869127
\(207\) −26465.5 + 615921.i −0.0429293 + 0.999078i
\(208\) −60127.3 −0.0963636
\(209\) 338602.i 0.536197i
\(210\) 609497. + 652240.i 0.953726 + 1.02061i
\(211\) 1.08224e6 1.67347 0.836737 0.547605i \(-0.184460\pi\)
0.836737 + 0.547605i \(0.184460\pi\)
\(212\) −84605.2 −0.129288
\(213\) 93325.7 87209.9i 0.140946 0.131709i
\(214\) 166494.i 0.248522i
\(215\) 794908.i 1.17279i
\(216\) −266801. 327370.i −0.389092 0.477425i
\(217\) 729896.i 1.05223i
\(218\) 832833. 1.18691
\(219\) −832763. 891162.i −1.17330 1.25559i
\(220\) −1.17958e6 −1.64313
\(221\) −227483. −0.313306
\(222\) −123492. 132152.i −0.168173 0.179966i
\(223\) 472939. 0.636859 0.318430 0.947947i \(-0.396845\pi\)
0.318430 + 0.947947i \(0.396845\pi\)
\(224\) 1.14350e6 1.52271
\(225\) 20744.5 305831.i 0.0273178 0.402741i
\(226\) 597913.i 0.778694i
\(227\) −410057. −0.528177 −0.264089 0.964498i \(-0.585071\pi\)
−0.264089 + 0.964498i \(0.585071\pi\)
\(228\) 282355. 263852.i 0.359715 0.336142i
\(229\) 395268.i 0.498085i 0.968493 + 0.249042i \(0.0801158\pi\)
−0.968493 + 0.249042i \(0.919884\pi\)
\(230\) 23773.1 + 959031.i 0.0296323 + 1.19540i
\(231\) −1.05376e6 + 984703.i −1.29930 + 1.21416i
\(232\) 781073. 0.952734
\(233\) 1.00983e6i 1.21859i 0.792944 + 0.609294i \(0.208547\pi\)
−0.792944 + 0.609294i \(0.791453\pi\)
\(234\) 280817. + 19047.7i 0.335261 + 0.0227407i
\(235\) 508614.i 0.600785i
\(236\) 344944.i 0.403151i
\(237\) 882434. 824606.i 1.02050 0.953621i
\(238\) 2.28214e6 2.61156
\(239\) 1.07223e6i 1.21421i −0.794623 0.607103i \(-0.792332\pi\)
0.794623 0.607103i \(-0.207668\pi\)
\(240\) 208918. + 223569.i 0.234125 + 0.250544i
\(241\) 1.41714e6i 1.57170i −0.618415 0.785851i \(-0.712225\pi\)
0.618415 0.785851i \(-0.287775\pi\)
\(242\) 1.85844e6i 2.03991i
\(243\) −531894. 751250.i −0.577843 0.816148i
\(244\) 54068.8i 0.0581397i
\(245\) 264556. 0.281581
\(246\) 21545.7 + 23056.7i 0.0226999 + 0.0242918i
\(247\) 73290.4i 0.0764372i
\(248\) 537328.i 0.554766i
\(249\) 181928. + 194687.i 0.185952 + 0.198993i
\(250\) 1.65867e6i 1.67846i
\(251\) −387993. −0.388722 −0.194361 0.980930i \(-0.562263\pi\)
−0.194361 + 0.980930i \(0.562263\pi\)
\(252\) −1.64226e6 111394.i −1.62907 0.110499i
\(253\) −1.54941e6 + 38407.7i −1.52183 + 0.0377240i
\(254\) 1.42198e6i 1.38296i
\(255\) 790414. + 845843.i 0.761209 + 0.814591i
\(256\) −190992. −0.182144
\(257\) 972339.i 0.918301i −0.888359 0.459150i \(-0.848154\pi\)
0.888359 0.459150i \(-0.151846\pi\)
\(258\) −1.71670e6 1.83709e6i −1.60563 1.71823i
\(259\) −200605. −0.185820
\(260\) 255320. 0.234235
\(261\) 1.69852e6 + 115210.i 1.54336 + 0.104686i
\(262\) −1.05582e6 −0.950246
\(263\) −1.47839e6 −1.31795 −0.658977 0.752163i \(-0.729011\pi\)
−0.658977 + 0.752163i \(0.729011\pi\)
\(264\) 775746. 724909.i 0.685030 0.640138i
\(265\) −81656.1 −0.0714289
\(266\) 735259.i 0.637142i
\(267\) 1.44701e6 + 1.54848e6i 1.24220 + 1.32932i
\(268\) 1.83784e6i 1.56304i
\(269\) 1.39260e6i 1.17340i 0.809805 + 0.586699i \(0.199573\pi\)
−0.809805 + 0.586699i \(0.800427\pi\)
\(270\) −904901. 1.11033e6i −0.755426 0.926925i
\(271\) −1.26005e6 −1.04223 −0.521115 0.853486i \(-0.674484\pi\)
−0.521115 + 0.853486i \(0.674484\pi\)
\(272\) 782253. 0.641099
\(273\) 228085. 213139.i 0.185221 0.173083i
\(274\) 2.84073e6i 2.28588i
\(275\) 770641. 0.614498
\(276\) −1.23939e6 1.26210e6i −0.979341 0.997288i
\(277\) 1.23028e6 0.963397 0.481699 0.876337i \(-0.340020\pi\)
0.481699 + 0.876337i \(0.340020\pi\)
\(278\) 1.47846e6i 1.14736i
\(279\) −79257.0 + 1.16847e6i −0.0609575 + 0.898683i
\(280\) −728878. −0.555597
\(281\) 2.37975e6 1.79790 0.898951 0.438050i \(-0.144331\pi\)
0.898951 + 0.438050i \(0.144331\pi\)
\(282\) −1.09842e6 1.17545e6i −0.822516 0.880198i
\(283\) 1.01299e6i 0.751863i 0.926647 + 0.375932i \(0.122677\pi\)
−0.926647 + 0.375932i \(0.877323\pi\)
\(284\) 366498.i 0.269635i
\(285\) 272513. 254655.i 0.198735 0.185712i
\(286\) 707609.i 0.511538i
\(287\) 34999.8 0.0250819
\(288\) −1.83060e6 124169.i −1.30051 0.0882132i
\(289\) 1.53969e6 1.08440
\(290\) 2.64915e6 1.84974
\(291\) −856287. + 800173.i −0.592771 + 0.553925i
\(292\) 3.49967e6 2.40198
\(293\) 1.28525e6 0.874618 0.437309 0.899311i \(-0.355932\pi\)
0.437309 + 0.899311i \(0.355932\pi\)
\(294\) −611410. + 571343.i −0.412538 + 0.385504i
\(295\) 332920.i 0.222733i
\(296\) 147680. 0.0979696
\(297\) 1.79386e6 1.46196e6i 1.18004 0.961709i
\(298\) 3.03505e6i 1.97982i
\(299\) 335369. 8313.34i 0.216943 0.00537771i
\(300\) 600513. + 642625.i 0.385229 + 0.412244i
\(301\) −2.78869e6 −1.77412
\(302\) 4.24212e6i 2.67649i
\(303\) 2.08026e6 1.94394e6i 1.30170 1.21640i
\(304\) 252026.i 0.156409i
\(305\) 52184.2i 0.0321210i
\(306\) −3.65341e6 247810.i −2.23046 0.151292i
\(307\) 440102. 0.266507 0.133253 0.991082i \(-0.457458\pi\)
0.133253 + 0.991082i \(0.457458\pi\)
\(308\) 4.13820e6i 2.48562i
\(309\) −688308. + 643201.i −0.410097 + 0.383222i
\(310\) 1.82244e6i 1.07708i
\(311\) 459889.i 0.269620i −0.990871 0.134810i \(-0.956958\pi\)
0.990871 0.134810i \(-0.0430424\pi\)
\(312\) −167910. + 156906.i −0.0976539 + 0.0912544i
\(313\) 2.79451e6i 1.61230i −0.591712 0.806149i \(-0.701548\pi\)
0.591712 0.806149i \(-0.298452\pi\)
\(314\) 1.13143e6 0.647597
\(315\) −1.58501e6 107511.i −0.900028 0.0610488i
\(316\) 3.46539e6i 1.95225i
\(317\) 2.26703e6i 1.26709i 0.773704 + 0.633547i \(0.218402\pi\)
−0.773704 + 0.633547i \(0.781598\pi\)
\(318\) 188713. 176347.i 0.104649 0.0977911i
\(319\) 4.27996e6i 2.35485i
\(320\) −2.22703e6 −1.21577
\(321\) −202299. 216486.i −0.109580 0.117265i
\(322\) −3.36447e6 + 83400.5i −1.80832 + 0.0448259i
\(323\) 953505.i 0.508530i
\(324\) 2.61694e6 + 356655.i 1.38494 + 0.188749i
\(325\) −166805. −0.0875993
\(326\) 473936.i 0.246988i
\(327\) −1.08290e6 + 1.01194e6i −0.560041 + 0.523340i
\(328\) −25765.8 −0.0132239
\(329\) −1.78432e6 −0.908830
\(330\) 2.63108e6 2.45866e6i 1.32999 1.24283i
\(331\) 85093.5 0.0426900 0.0213450 0.999772i \(-0.493205\pi\)
0.0213450 + 0.999772i \(0.493205\pi\)
\(332\) −764551. −0.380681
\(333\) 321143. + 21783.1i 0.158704 + 0.0107649i
\(334\) −406075. −0.199177
\(335\) 1.77378e6i 0.863551i
\(336\) −784324. + 732926.i −0.379007 + 0.354170i
\(337\) 2.25704e6i 1.08259i −0.840832 0.541297i \(-0.817934\pi\)
0.840832 0.541297i \(-0.182066\pi\)
\(338\) 3.09916e6i 1.47554i
\(339\) 726496. + 777443.i 0.343347 + 0.367426i
\(340\) −3.32170e6 −1.55834
\(341\) −2.94434e6 −1.37120
\(342\) −79839.3 + 1.17705e6i −0.0369106 + 0.544165i
\(343\) 1.61721e6i 0.742218i
\(344\) 2.05295e6 0.935368
\(345\) −1.19618e6 1.21811e6i −0.541066 0.550982i
\(346\) 3.25723e6 1.46271
\(347\) 895437.i 0.399219i −0.979876 0.199610i \(-0.936033\pi\)
0.979876 0.199610i \(-0.0639674\pi\)
\(348\) −3.56899e6 + 3.33511e6i −1.57978 + 1.47626i
\(349\) 1.69659e6 0.745614 0.372807 0.927909i \(-0.378395\pi\)
0.372807 + 0.927909i \(0.378395\pi\)
\(350\) 1.67341e6 0.730183
\(351\) −388279. + 316440.i −0.168220 + 0.137096i
\(352\) 4.61280e6i 1.98430i
\(353\) 603075.i 0.257593i −0.991671 0.128797i \(-0.958889\pi\)
0.991671 0.128797i \(-0.0411114\pi\)
\(354\) 718983. + 769404.i 0.304937 + 0.326322i
\(355\) 353723.i 0.148968i
\(356\) −6.08103e6 −2.54303
\(357\) −2.96738e6 + 2.77292e6i −1.23226 + 1.15151i
\(358\) 2.80337e6 1.15604
\(359\) −3.74407e6 −1.53323 −0.766617 0.642105i \(-0.778061\pi\)
−0.766617 + 0.642105i \(0.778061\pi\)
\(360\) 1.16684e6 + 79146.5i 0.474520 + 0.0321866i
\(361\) 2.16890e6 0.875934
\(362\) −4.48970e6 −1.80072
\(363\) 2.25811e6 + 2.41647e6i 0.899453 + 0.962529i
\(364\) 895712.i 0.354336i
\(365\) 3.37768e6 1.32705
\(366\) −112698. 120602.i −0.0439759 0.0470598i
\(367\) 4.16068e6i 1.61250i −0.591577 0.806249i \(-0.701494\pi\)
0.591577 0.806249i \(-0.298506\pi\)
\(368\) −1.15324e6 + 28587.3i −0.443917 + 0.0110041i
\(369\) −56030.2 3800.52i −0.0214218 0.00145304i
\(370\) 500882. 0.190209
\(371\) 286465.i 0.108053i
\(372\) −2.29434e6 2.45523e6i −0.859607 0.919890i
\(373\) 3.99193e6i 1.48563i −0.669496 0.742816i \(-0.733490\pi\)
0.669496 0.742816i \(-0.266510\pi\)
\(374\) 9.20596e6i 3.40322i
\(375\) 2.01537e6 + 2.15671e6i 0.740078 + 0.791978i
\(376\) 1.31356e6 0.479161
\(377\) 926396.i 0.335694i
\(378\) 3.89527e6 3.17457e6i 1.40219 1.14276i
\(379\) 98283.1i 0.0351464i −0.999846 0.0175732i \(-0.994406\pi\)
0.999846 0.0175732i \(-0.00559401\pi\)
\(380\) 1.07018e6i 0.380189i
\(381\) −1.72778e6 1.84895e6i −0.609785 0.652547i
\(382\) 2.36489e6i 0.829186i
\(383\) −2.81372e6 −0.980130 −0.490065 0.871686i \(-0.663027\pi\)
−0.490065 + 0.871686i \(0.663027\pi\)
\(384\) 2.39487e6 2.23793e6i 0.828807 0.774494i
\(385\) 3.99395e6i 1.37326i
\(386\) 5.47061e6i 1.86882i
\(387\) 4.46433e6 + 302815.i 1.51523 + 0.102778i
\(388\) 3.36271e6i 1.13399i
\(389\) 2.68573e6 0.899889 0.449944 0.893057i \(-0.351444\pi\)
0.449944 + 0.893057i \(0.351444\pi\)
\(390\) −569496. + 532176.i −0.189596 + 0.177171i
\(391\) −4.36314e6 + 108156.i −1.44330 + 0.0357775i
\(392\) 683251.i 0.224577i
\(393\) 1.37284e6 1.28288e6i 0.448372 0.418990i
\(394\) −6.42924e6 −2.08650
\(395\) 3.34460e6i 1.07858i
\(396\) −449354. + 6.62472e6i −0.143996 + 2.12290i
\(397\) 3.49044e6 1.11149 0.555743 0.831354i \(-0.312434\pi\)
0.555743 + 0.831354i \(0.312434\pi\)
\(398\) 7.85065e6 2.48427
\(399\) 893379. + 956029.i 0.280933 + 0.300635i
\(400\) 573597. 0.179249
\(401\) 1.45743e6 0.452613 0.226307 0.974056i \(-0.427335\pi\)
0.226307 + 0.974056i \(0.427335\pi\)
\(402\) 3.83071e6 + 4.09934e6i 1.18226 + 1.26517i
\(403\) 637300. 0.195471
\(404\) 8.16936e6i 2.49020i
\(405\) 2.52572e6 + 344223.i 0.765153 + 0.104280i
\(406\) 9.29372e6i 2.79817i
\(407\) 809224.i 0.242149i
\(408\) 2.18450e6 2.04134e6i 0.649683 0.607108i
\(409\) −397052. −0.117365 −0.0586825 0.998277i \(-0.518690\pi\)
−0.0586825 + 0.998277i \(0.518690\pi\)
\(410\) −87389.4 −0.0256743
\(411\) −3.45164e6 3.69370e6i −1.00791 1.07859i
\(412\) 2.70304e6i 0.784531i
\(413\) 1.16795e6 0.336937
\(414\) 5.39513e6 + 231823.i 1.54704 + 0.0664746i
\(415\) −737901. −0.210319
\(416\) 998439.i 0.282871i
\(417\) 1.79641e6 + 1.92239e6i 0.505901 + 0.541379i
\(418\) −2.96597e6 −0.830283
\(419\) −4.90111e6 −1.36383 −0.681913 0.731433i \(-0.738852\pi\)
−0.681913 + 0.731433i \(0.738852\pi\)
\(420\) 3.33049e6 3.11224e6i 0.921267 0.860895i
\(421\) 4.82268e6i 1.32612i 0.748566 + 0.663061i \(0.230743\pi\)
−0.748566 + 0.663061i \(0.769257\pi\)
\(422\) 9.47985e6i 2.59132i
\(423\) 2.85646e6 + 193753.i 0.776207 + 0.0526500i
\(424\) 210887.i 0.0569687i
\(425\) 2.17013e6 0.582791
\(426\) −763910. 817481.i −0.203947 0.218250i
\(427\) −183072. −0.0485906
\(428\) 850159. 0.224332
\(429\) −859783. 920077.i −0.225551 0.241369i
\(430\) 6.96295e6 1.81603
\(431\) 3.02169e6 0.783533 0.391767 0.920065i \(-0.371864\pi\)
0.391767 + 0.920065i \(0.371864\pi\)
\(432\) 1.33519e6 1.08815e6i 0.344217 0.280531i
\(433\) 3.30312e6i 0.846650i −0.905978 0.423325i \(-0.860863\pi\)
0.905978 0.423325i \(-0.139137\pi\)
\(434\) −6.39348e6 −1.62934
\(435\) −3.44459e6 + 3.21886e6i −0.872799 + 0.815602i
\(436\) 4.25265e6i 1.07138i
\(437\) 34845.7 + 1.40571e6i 0.00872862 + 0.352122i
\(438\) −7.80609e6 + 7.29454e6i −1.94423 + 1.81682i
\(439\) −3.90756e6 −0.967708 −0.483854 0.875149i \(-0.660763\pi\)
−0.483854 + 0.875149i \(0.660763\pi\)
\(440\) 2.94023e6i 0.724019i
\(441\) 100781. 1.48579e6i 0.0246764 0.363799i
\(442\) 1.99263e6i 0.485143i
\(443\) 2.12284e6i 0.513934i −0.966420 0.256967i \(-0.917277\pi\)
0.966420 0.256967i \(-0.0827231\pi\)
\(444\) −674799. + 630578.i −0.162449 + 0.151803i
\(445\) −5.86906e6 −1.40497
\(446\) 4.14269e6i 0.986154i
\(447\) −3.68775e6 3.94636e6i −0.872956 0.934174i
\(448\) 7.81284e6i 1.83914i
\(449\) 551494.i 0.129100i −0.997914 0.0645499i \(-0.979439\pi\)
0.997914 0.0645499i \(-0.0205612\pi\)
\(450\) −2.67891e6 181710.i −0.623630 0.0423007i
\(451\) 141186.i 0.0326852i
\(452\) −3.05309e6 −0.702899
\(453\) −5.15440e6 5.51586e6i −1.18014 1.26290i
\(454\) 3.59187e6i 0.817864i
\(455\) 864490.i 0.195763i
\(456\) −657679. 703800.i −0.148116 0.158503i
\(457\) 146258.i 0.0327590i 0.999866 + 0.0163795i \(0.00521398\pi\)
−0.999866 + 0.0163795i \(0.994786\pi\)
\(458\) 3.46233e6 0.771267
\(459\) 5.05150e6 4.11687e6i 1.11915 0.912086i
\(460\) 4.89704e6 121391.i 1.07904 0.0267480i
\(461\) 5.82484e6i 1.27653i −0.769816 0.638266i \(-0.779652\pi\)
0.769816 0.638266i \(-0.220348\pi\)
\(462\) 8.62545e6 + 9.23033e6i 1.88008 + 2.01193i
\(463\) 4.42318e6 0.958920 0.479460 0.877564i \(-0.340833\pi\)
0.479460 + 0.877564i \(0.340833\pi\)
\(464\) 3.18563e6i 0.686910i
\(465\) −2.21436e6 2.36965e6i −0.474916 0.508221i
\(466\) 8.84552e6 1.88694
\(467\) −1.31195e6 −0.278371 −0.139185 0.990266i \(-0.544448\pi\)
−0.139185 + 0.990266i \(0.544448\pi\)
\(468\) 97262.4 1.43392e6i 0.0205272 0.302628i
\(469\) 6.22277e6 1.30633
\(470\) 4.45518e6 0.930295
\(471\) −1.47116e6 + 1.37475e6i −0.305568 + 0.285543i
\(472\) −859809. −0.177643
\(473\) 1.12493e7i 2.31193i
\(474\) −7.22309e6 7.72963e6i −1.47665 1.58020i
\(475\) 699169.i 0.142183i
\(476\) 1.16532e7i 2.35736i
\(477\) −31106.3 + 458594.i −0.00625969 + 0.0922853i
\(478\) −9.39212e6 −1.88016
\(479\) −491382. −0.0978545 −0.0489273 0.998802i \(-0.515580\pi\)
−0.0489273 + 0.998802i \(0.515580\pi\)
\(480\) 3.71246e6 3.46918e6i 0.735460 0.687264i
\(481\) 175156.i 0.0345194i
\(482\) −1.24134e7 −2.43373
\(483\) 4.27335e6 4.19645e6i 0.833491 0.818491i
\(484\) −9.48967e6 −1.84136
\(485\) 3.24550e6i 0.626509i
\(486\) −6.58054e6 + 4.65910e6i −1.26378 + 0.894770i
\(487\) −2.13183e6 −0.407315 −0.203657 0.979042i \(-0.565283\pi\)
−0.203657 + 0.979042i \(0.565283\pi\)
\(488\) 134772. 0.0256184
\(489\) −575858. 616241.i −0.108904 0.116541i
\(490\) 2.31737e6i 0.436018i
\(491\) 4.98864e6i 0.933854i 0.884296 + 0.466927i \(0.154639\pi\)
−0.884296 + 0.466927i \(0.845361\pi\)
\(492\) 117733. 110018.i 0.0219273 0.0204904i
\(493\) 1.20524e7i 2.23334i
\(494\) 641983. 0.118360
\(495\) −433690. + 6.39380e6i −0.0795549 + 1.17286i
\(496\) −2.19150e6 −0.399980
\(497\) −1.24093e6 −0.225349
\(498\) 1.70535e6 1.59359e6i 0.308134 0.287941i
\(499\) 3.54759e6 0.637797 0.318898 0.947789i \(-0.396687\pi\)
0.318898 + 0.947789i \(0.396687\pi\)
\(500\) −8.46958e6 −1.51508
\(501\) 528004. 493403.i 0.0939816 0.0878228i
\(502\) 3.39860e6i 0.601923i
\(503\) −442972. −0.0780651 −0.0390325 0.999238i \(-0.512428\pi\)
−0.0390325 + 0.999238i \(0.512428\pi\)
\(504\) −277661. + 4.09350e6i −0.0486899 + 0.717825i
\(505\) 7.88460e6i 1.37579i
\(506\) 336430. + 1.35720e7i 0.0584143 + 2.35649i
\(507\) −3.76564e6 4.02972e6i −0.650608 0.696233i
\(508\) 7.26098e6 1.24835
\(509\) 5.88309e6i 1.00649i −0.864143 0.503247i \(-0.832139\pi\)
0.864143 0.503247i \(-0.167861\pi\)
\(510\) 7.40912e6 6.92358e6i 1.26137 1.17871i
\(511\) 1.18496e7i 2.00748i
\(512\) 5.05561e6i 0.852311i
\(513\) −1.32637e6 1.62749e6i −0.222521 0.273039i
\(514\) −8.51715e6 −1.42196
\(515\) 2.60882e6i 0.433438i
\(516\) −9.38064e6 + 8.76591e6i −1.55099 + 1.44935i
\(517\) 7.19778e6i 1.18433i
\(518\) 1.75719e6i 0.287736i
\(519\) −4.23526e6 + 3.95771e6i −0.690179 + 0.644950i
\(520\) 636412.i 0.103212i
\(521\) 8.70774e6 1.40544 0.702718 0.711468i \(-0.251969\pi\)
0.702718 + 0.711468i \(0.251969\pi\)
\(522\) 1.00918e6 1.48780e7i 0.162103 2.38984i
\(523\) 4.34219e6i 0.694153i 0.937837 + 0.347076i \(0.112826\pi\)
−0.937837 + 0.347076i \(0.887174\pi\)
\(524\) 5.39127e6i 0.857754i
\(525\) −2.17587e6 + 2.03328e6i −0.344536 + 0.321958i
\(526\) 1.29499e7i 2.04081i
\(527\) −8.29125e6 −1.30045
\(528\) 2.95656e6 + 3.16390e6i 0.461532 + 0.493898i
\(529\) 6.42844e6 318900.i 0.998772 0.0495468i
\(530\) 715262.i 0.110605i
\(531\) −1.86973e6 126824.i −0.287769 0.0195193i
\(532\) −3.75441e6 −0.575125
\(533\) 30559.7i 0.00465941i
\(534\) 1.35638e7 1.26750e7i 2.05840 1.92351i
\(535\) 820525. 0.123939
\(536\) −4.58102e6 −0.688732
\(537\) −3.64511e6 + 3.40624e6i −0.545475 + 0.509729i
\(538\) 1.21984e7 1.81697
\(539\) 3.74394e6 0.555081
\(540\) −5.66964e6 + 4.62065e6i −0.836702 + 0.681896i
\(541\) 9.64282e6 1.41648 0.708241 0.705971i \(-0.249489\pi\)
0.708241 + 0.705971i \(0.249489\pi\)
\(542\) 1.10373e7i 1.61386i
\(543\) 5.83779e6 5.45523e6i 0.849668 0.793987i
\(544\) 1.29896e7i 1.88192i
\(545\) 4.10441e6i 0.591916i
\(546\) −1.86698e6 1.99790e6i −0.268014 0.286809i
\(547\) −4.65385e6 −0.665034 −0.332517 0.943097i \(-0.607898\pi\)
−0.332517 + 0.943097i \(0.607898\pi\)
\(548\) 1.45055e7 2.06339
\(549\) 293075. + 19879.2i 0.0415000 + 0.00281493i
\(550\) 6.75039e6i 0.951529i
\(551\) 3.88302e6 0.544868
\(552\) −3.14592e6 + 3.08930e6i −0.439440 + 0.431532i
\(553\) −1.17335e7 −1.63161
\(554\) 1.07766e7i 1.49179i
\(555\) −651278. + 608598.i −0.0897499 + 0.0838684i
\(556\) −7.54940e6 −1.03568
\(557\) 1.19450e7 1.63136 0.815680 0.578504i \(-0.196363\pi\)
0.815680 + 0.578504i \(0.196363\pi\)
\(558\) 1.02351e7 + 694247.i 1.39158 + 0.0943906i
\(559\) 2.43491e6i 0.329575i
\(560\) 2.97275e6i 0.400579i
\(561\) 1.11857e7 + 1.19702e7i 1.50057 + 1.60581i
\(562\) 2.08453e7i 2.78399i
\(563\) 5.15603e6 0.685558 0.342779 0.939416i \(-0.388632\pi\)
0.342779 + 0.939416i \(0.388632\pi\)
\(564\) −6.00212e6 + 5.60879e6i −0.794523 + 0.742457i
\(565\) −2.94667e6 −0.388338
\(566\) 8.87322e6 1.16423
\(567\) −1.20760e6 + 8.86073e6i −0.157749 + 1.15748i
\(568\) 913536. 0.118810
\(569\) −1.87013e6 −0.242154 −0.121077 0.992643i \(-0.538635\pi\)
−0.121077 + 0.992643i \(0.538635\pi\)
\(570\) −2.23063e6 2.38706e6i −0.287569 0.307735i
\(571\) 7.63524e6i 0.980015i 0.871718 + 0.490007i \(0.163006\pi\)
−0.871718 + 0.490007i \(0.836994\pi\)
\(572\) 3.61322e6 0.461748
\(573\) −2.87347e6 3.07497e6i −0.365611 0.391251i
\(574\) 306579.i 0.0388385i
\(575\) −3.19933e6 + 79306.9i −0.403542 + 0.0100033i
\(576\) −848371. + 1.25073e7i −0.106544 + 1.57076i
\(577\) −3.94420e6 −0.493196 −0.246598 0.969118i \(-0.579313\pi\)
−0.246598 + 0.969118i \(0.579313\pi\)
\(578\) 1.34868e7i 1.67915i
\(579\) −6.64708e6 7.11322e6i −0.824014 0.881800i
\(580\) 1.35272e7i 1.66970i
\(581\) 2.58870e6i 0.318157i
\(582\) 7.00907e6 + 7.50060e6i 0.857735 + 0.917885i
\(583\) −1.15558e6 −0.140808
\(584\) 8.72330e6i 1.05840i
\(585\) 93872.1 1.38394e6i 0.0113409 0.167196i
\(586\) 1.12581e7i 1.35432i
\(587\) 1.46795e7i 1.75839i 0.476464 + 0.879194i \(0.341918\pi\)
−0.476464 + 0.879194i \(0.658082\pi\)
\(588\) 2.91742e6 + 3.12201e6i 0.347981 + 0.372384i
\(589\) 2.67127e6i 0.317270i
\(590\) −2.91619e6 −0.344895
\(591\) 8.35970e6 7.81187e6i 0.984514 0.919997i
\(592\) 602315.i 0.0706349i
\(593\) 9.13831e6i 1.06716i 0.845750 + 0.533580i \(0.179154\pi\)
−0.845750 + 0.533580i \(0.820846\pi\)
\(594\) −1.28059e7 1.57132e7i −1.48917 1.82725i
\(595\) 1.12470e7i 1.30240i
\(596\) 1.54977e7 1.78711
\(597\) −1.02079e7 + 9.53896e6i −1.17220 + 1.09538i
\(598\) −72820.2 2.93765e6i −0.00832720 0.335928i
\(599\) 7.63288e6i 0.869203i −0.900623 0.434602i \(-0.856889\pi\)
0.900623 0.434602i \(-0.143111\pi\)
\(600\) 1.60181e6 1.49684e6i 0.181649 0.169745i
\(601\) −7.47363e6 −0.844006 −0.422003 0.906594i \(-0.638673\pi\)
−0.422003 + 0.906594i \(0.638673\pi\)
\(602\) 2.44274e7i 2.74717i
\(603\) −9.96185e6 675710.i −1.11570 0.0756776i
\(604\) 2.16613e7 2.41597
\(605\) −9.15889e6 −1.01731
\(606\) −1.70278e7 1.82219e7i −1.88355 2.01564i
\(607\) 7.40886e6 0.816168 0.408084 0.912944i \(-0.366197\pi\)
0.408084 + 0.912944i \(0.366197\pi\)
\(608\) −4.18499e6 −0.459130
\(609\) −1.12924e7 1.20843e7i −1.23379 1.32032i
\(610\) 457104. 0.0497383
\(611\) 1.55796e6i 0.168831i
\(612\) −1.26538e6 + 1.86552e7i −0.136566 + 2.01336i
\(613\) 1.25160e7i 1.34528i −0.739969 0.672641i \(-0.765160\pi\)
0.739969 0.672641i \(-0.234840\pi\)
\(614\) 3.85505e6i 0.412676i
\(615\) 113629. 106183.i 0.0121144 0.0113205i
\(616\) −1.03149e7 −1.09525
\(617\) −4.97604e6 −0.526225 −0.263112 0.964765i \(-0.584749\pi\)
−0.263112 + 0.964765i \(0.584749\pi\)
\(618\) 5.63409e6 + 6.02919e6i 0.593406 + 0.635021i
\(619\) 5.54618e6i 0.581792i 0.956755 + 0.290896i \(0.0939534\pi\)
−0.956755 + 0.290896i \(0.906047\pi\)
\(620\) 9.30583e6 0.972246
\(621\) −7.29676e6 + 6.25394e6i −0.759279 + 0.650766i
\(622\) −4.02838e6 −0.417498
\(623\) 2.05898e7i 2.12536i
\(624\) −639946. 684824.i −0.0657933 0.0704073i
\(625\) −4.23230e6 −0.433388
\(626\) −2.44784e7 −2.49659
\(627\) 3.85654e6 3.60381e6i 0.391768 0.366095i
\(628\) 5.77737e6i 0.584563i
\(629\) 2.27878e6i 0.229654i
\(630\) −941737. + 1.38838e7i −0.0945319 + 1.39366i
\(631\) 3.82572e6i 0.382507i 0.981541 + 0.191254i \(0.0612553\pi\)
−0.981541 + 0.191254i \(0.938745\pi\)
\(632\) 8.63786e6 0.860228
\(633\) 1.15185e7 + 1.23263e7i 1.14258 + 1.22271i
\(634\) 1.98579e7 1.96205
\(635\) 7.00788e6 0.689688
\(636\) −900469. 963617.i −0.0882726 0.0944630i
\(637\) −810374. −0.0791292
\(638\) 3.74901e7 3.64640
\(639\) 1.98657e6 + 134748.i 0.192465 + 0.0130548i
\(640\) 9.07703e6i 0.875979i
\(641\) 4.33390e6 0.416614 0.208307 0.978063i \(-0.433205\pi\)
0.208307 + 0.978063i \(0.433205\pi\)
\(642\) −1.89630e6 + 1.77203e6i −0.181580 + 0.169681i
\(643\) 1.11605e7i 1.06453i −0.846578 0.532265i \(-0.821341\pi\)
0.846578 0.532265i \(-0.178659\pi\)
\(644\) 425863. + 1.71798e7i 0.0404628 + 1.63231i
\(645\) −9.05366e6 + 8.46036e6i −0.856890 + 0.800736i
\(646\) −8.35217e6 −0.787441
\(647\) 3.89565e6i 0.365863i −0.983126 0.182932i \(-0.941441\pi\)
0.983126 0.182932i \(-0.0585587\pi\)
\(648\) 888999. 6.52301e6i 0.0831695 0.610254i
\(649\) 4.71140e6i 0.439075i
\(650\) 1.46112e6i 0.135644i
\(651\) 8.31320e6 7.76842e6i 0.768804 0.718423i
\(652\) 2.42003e6 0.222947
\(653\) 1.74450e6i 0.160099i 0.996791 + 0.0800495i \(0.0255078\pi\)
−0.996791 + 0.0800495i \(0.974492\pi\)
\(654\) 8.86400e6 + 9.48561e6i 0.810374 + 0.867204i
\(655\) 5.20334e6i 0.473892i
\(656\) 105087.i 0.00953428i
\(657\) 1.28671e6 1.89696e7i 0.116296 1.71453i
\(658\) 1.56296e7i 1.40729i
\(659\) −732273. −0.0656839 −0.0328420 0.999461i \(-0.510456\pi\)
−0.0328420 + 0.999461i \(0.510456\pi\)
\(660\) −1.25545e7 1.34349e7i −1.12186 1.20054i
\(661\) 6.40243e6i 0.569956i −0.958534 0.284978i \(-0.908014\pi\)
0.958534 0.284978i \(-0.0919863\pi\)
\(662\) 745372.i 0.0661041i
\(663\) −2.42115e6 2.59094e6i −0.213913 0.228914i
\(664\) 1.90572e6i 0.167741i
\(665\) −3.62354e6 −0.317745
\(666\) 190808. 2.81303e6i 0.0166690 0.245748i
\(667\) −440452. 1.77683e7i −0.0383340 1.54643i
\(668\) 2.07352e6i 0.179790i
\(669\) 5.03359e6 + 5.38658e6i 0.434823 + 0.465316i
\(670\) −1.55373e7 −1.33718
\(671\) 738497.i 0.0633203i
\(672\) 1.21705e7 + 1.30240e7i 1.03965 + 1.11256i
\(673\) −1.55698e7 −1.32509 −0.662546 0.749021i \(-0.730524\pi\)
−0.662546 + 0.749021i \(0.730524\pi\)
\(674\) −1.97704e7 −1.67636
\(675\) 3.70407e6 3.01875e6i 0.312911 0.255016i
\(676\) 1.58251e7 1.33192
\(677\) 445662. 0.0373710 0.0186855 0.999825i \(-0.494052\pi\)
0.0186855 + 0.999825i \(0.494052\pi\)
\(678\) 6.80997e6 6.36370e6i 0.568946 0.531662i
\(679\) 1.13858e7 0.947743
\(680\) 8.27969e6i 0.686660i
\(681\) −4.36432e6 4.67038e6i −0.360619 0.385908i
\(682\) 2.57907e7i 2.12326i
\(683\) 5.85494e6i 0.480254i 0.970741 + 0.240127i \(0.0771891\pi\)
−0.970741 + 0.240127i \(0.922811\pi\)
\(684\) 6.01032e6 + 407679.i 0.491199 + 0.0333179i
\(685\) 1.39999e7 1.13998
\(686\) −1.41659e7 −1.14930
\(687\) −4.50194e6 + 4.20692e6i −0.363921 + 0.340073i
\(688\) 8.37301e6i 0.674389i
\(689\) 250124. 0.0200728
\(690\) −1.06699e7 + 1.04779e7i −0.853177 + 0.837823i
\(691\) 801751. 0.0638770 0.0319385 0.999490i \(-0.489832\pi\)
0.0319385 + 0.999490i \(0.489832\pi\)
\(692\) 1.66322e7i 1.32034i
\(693\) −2.24307e7 1.52147e6i −1.77423 0.120346i
\(694\) −7.84353e6 −0.618177
\(695\) −7.28625e6 −0.572192
\(696\) 8.31311e6 + 8.89609e6i 0.650490 + 0.696107i
\(697\) 397581.i 0.0309987i
\(698\) 1.48612e7i 1.15456i
\(699\) −1.15015e7 + 1.07478e7i −0.890351 + 0.832004i
\(700\) 8.54483e6i 0.659111i
\(701\) 2.12413e7 1.63263 0.816313 0.577610i \(-0.196015\pi\)
0.816313 + 0.577610i \(0.196015\pi\)
\(702\) 2.77184e6 + 3.40111e6i 0.212288 + 0.260482i
\(703\) 734174. 0.0560287
\(704\) −3.15163e7 −2.39665
\(705\) −5.79290e6 + 5.41328e6i −0.438958 + 0.410193i
\(706\) −5.28260e6 −0.398874
\(707\) −2.76607e7 −2.08121
\(708\) 3.92876e6 3.67130e6i 0.294559 0.275256i
\(709\) 3.90485e6i 0.291735i 0.989304 + 0.145868i \(0.0465974\pi\)
−0.989304 + 0.145868i \(0.953403\pi\)
\(710\) 3.09842e6 0.230672
\(711\) 1.87838e7 + 1.27410e6i 1.39351 + 0.0945215i
\(712\) 1.51576e7i 1.12055i
\(713\) 1.22234e7 303002.i 0.900471 0.0223214i
\(714\) 2.42893e7 + 2.59926e7i 1.78307 + 1.90811i
\(715\) 3.48728e6 0.255106
\(716\) 1.43147e7i 1.04352i
\(717\) 1.22122e7 1.14119e7i 0.887149 0.829013i
\(718\) 3.27960e7i 2.37416i
\(719\) 1.90699e7i 1.37571i 0.725848 + 0.687855i \(0.241448\pi\)
−0.725848 + 0.687855i \(0.758552\pi\)
\(720\) −322801. + 4.75898e6i −0.0232062 + 0.342123i
\(721\) 9.15226e6 0.655677
\(722\) 1.89984e7i 1.35635i
\(723\) 1.61406e7 1.50829e7i 1.14835 1.07310i
\(724\) 2.29255e7i 1.62545i
\(725\) 8.83756e6i 0.624435i
\(726\) 2.11669e7 1.97798e7i 1.49044 1.39277i
\(727\) 1.09662e7i 0.769522i 0.923016 + 0.384761i \(0.125716\pi\)
−0.923016 + 0.384761i \(0.874284\pi\)
\(728\) 2.23266e6 0.156133
\(729\) 2.89537e6 1.40538e7i 0.201783 0.979430i
\(730\) 2.95866e7i 2.05489i
\(731\) 3.16781e7i 2.19263i
\(732\) −615821. + 575465.i −0.0424793 + 0.0396955i
\(733\) 945012.i 0.0649647i 0.999472 + 0.0324824i \(0.0103413\pi\)
−0.999472 + 0.0324824i \(0.989659\pi\)
\(734\) −3.64452e7 −2.49690
\(735\) 2.81573e6 + 3.01319e6i 0.192252 + 0.205735i
\(736\) 474705. + 1.91501e7i 0.0323020 + 1.30310i
\(737\) 2.51021e7i 1.70232i
\(738\) −33290.4 + 490793.i −0.00224998 + 0.0331709i
\(739\) −2.68786e7 −1.81049 −0.905243 0.424894i \(-0.860311\pi\)
−0.905243 + 0.424894i \(0.860311\pi\)
\(740\) 2.55762e6i 0.171695i
\(741\) −834746. + 780044.i −0.0558482 + 0.0521883i
\(742\) −2.50928e6 −0.167317
\(743\) 1.24569e7 0.827825 0.413912 0.910317i \(-0.364162\pi\)
0.413912 + 0.910317i \(0.364162\pi\)
\(744\) −6.11993e6 + 5.71888e6i −0.405335 + 0.378773i
\(745\) 1.49575e7 0.987343
\(746\) −3.49671e7 −2.30045
\(747\) −281098. + 4.14417e6i −0.0184313 + 0.271729i
\(748\) −4.70079e7 −3.07197
\(749\) 2.87856e6i 0.187487i
\(750\) 1.88916e7 1.76536e7i 1.22635 1.14599i
\(751\) 5.77627e6i 0.373721i −0.982386 0.186861i \(-0.940169\pi\)
0.982386 0.186861i \(-0.0598313\pi\)
\(752\) 5.35739e6i 0.345469i
\(753\) −4.12948e6 4.41907e6i −0.265404 0.284017i
\(754\) −8.11471e6 −0.519810
\(755\) 2.09062e7 1.33478
\(756\) −1.62101e7 1.98902e7i −1.03153 1.26571i
\(757\) 8.56985e6i 0.543542i −0.962362 0.271771i \(-0.912391\pi\)
0.962362 0.271771i \(-0.0876094\pi\)
\(758\) −860906. −0.0544230
\(759\) −1.69281e7 1.72383e7i −1.06661 1.08615i
\(760\) 2.66755e6 0.167524
\(761\) 1.26939e7i 0.794570i −0.917695 0.397285i \(-0.869952\pi\)
0.917695 0.397285i \(-0.130048\pi\)
\(762\) −1.61957e7 + 1.51344e7i −1.01045 + 0.944230i
\(763\) 1.43991e7 0.895413
\(764\) 1.20757e7 0.748477
\(765\) −1.22127e6 + 1.80049e7i −0.0754500 + 1.11234i
\(766\) 2.46466e7i 1.51770i
\(767\) 1.01978e6i 0.0625919i
\(768\) −2.03276e6 2.17531e6i −0.124361 0.133082i
\(769\) 216230.i 0.0131856i −0.999978 0.00659281i \(-0.997901\pi\)
0.999978 0.00659281i \(-0.00209857\pi\)
\(770\) −3.49848e7 −2.12644
\(771\) 1.10745e7 1.03488e7i 0.670949 0.626980i
\(772\) 2.79343e7 1.68692
\(773\) −2.26652e7 −1.36430 −0.682150 0.731212i \(-0.738955\pi\)
−0.682150 + 0.731212i \(0.738955\pi\)
\(774\) 2.65249e6 3.91051e7i 0.159148 2.34628i
\(775\) −6.07966e6 −0.363601
\(776\) −8.38192e6 −0.499677
\(777\) −2.13508e6 2.28481e6i −0.126871